Bitcoin: A Peer-to-Peer Electronic Cash System by Satoshi Nakamoto
Abstract. A purely peer-to-peer version of electronic
cash would allow online payments to be sent directly from one party
to another without going through a financial institution. Digital signatures
provide part of the solution, but the main benefits are lost if a trusted third party
is still required to prevent double-spending. We propose a solution to the double-spending
problem using a peer-to-peer network. The network timestamps transactions by hashing
them into an ongoing chain of hash-based proof-of-work, forming a record
that cannot be changed without redoing the proof-of-work. The longest chain not only
serves as proof of the sequence of events witnessed, but proof that it came from
the largest pool of CPU power. As long as a majority of CPU power is controlled
by nodes that are not cooperating to attack the network, they'll generate the longest
chain and outpace attackers. The network itself requires minimal structure.
Messages are broadcast on a best effort basis, and nodes can leave and rejoin the
network at will, accepting the longest proof-of-work chain as proof of what happened
while they were gone.
1. Introduction Commerce on the Internet has come to rely
almost exclusively on financial institutions serving as
trusted third parties to process electronic payments. While the system works well enough
for most transactions, it still suffers from the
inherent weaknesses of the trust based model. Completely non-reversible transactions are
not really possible, since financial institutions cannot
avoid mediating disputes. The cost of mediation increases transaction costs, limiting the
minimum practical transaction size and cutting off the possibility for small casual transactions,
and there is a broader cost in the loss of ability to make non-reversible payments for
non- reversible services. With the possibility
of reversal, the need for trust spreads. Merchants must
be wary of their customers, hassling them for more information than they would otherwise
need. A certain percentage of fraud is accepted
as unavoidable. These costs and payment uncertainties can be avoided in person by using physical
currency, but no mechanism exists to make payments
over a communications channel without a trusted party.
What is needed is an electronic payment system based on cryptographic proof instead of trust,
allowing any two willing parties to transact directly with each other without the need
for a trusted third party. Transactions that are computationally
impractical to reverse would protect sellers from fraud, and routine escrow mechanisms
could easily be implemented to protect buyers. In
this paper, we propose a solution to the double-spending problem using a peer-to-peer distributed
timestamp server to generate computational proof of the chronological order of transactions.
The system is secure as long as honest nodes collectively
control more CPU power than any cooperating group of attacker nodes.
2.Transactions
We define an electronic coin as a chain of digital signatures. Each owner transfers the
coin to the next by digitally signing a hash of the previous
transaction and the public key of the next owner
and adding these to the end of the coin. A payee can verify the signatures to verify
the chain of ownership.
The problem of course is the payee can't verify that one of the owners did not double-spend
the coin. A common solution is to introduce a trusted central authority, or mint, that
checks every transaction for double spending. After each
transaction, the coin must be returned to the mint to
issue a new coin, and only coins issued directly from the mint are trusted not to be double-spent.
The problem with this solution is that the fate of the entire money system depends on
the company running the mint, with every transaction
having to go through them, just like a bank. We need a way for the payee to know that the
previous owners did not sign any earlier transactions. For our purposes, the earliest
transaction is the one that counts, so we don't care
about later attempts to double-spend. The only way to confirm the absence of a transaction
is to be aware of all transactions. In the mint
based model, the mint was aware of all transactions and
decided which arrived first. To accomplish this without a trusted party, transactions
must be publicly announced, and we need a system for
participants to agree on a single history of the
order in which they were received. The payee needs proof that at the time of each transaction,
the majority of nodes agreed it was the first
received.
3.Timestamp Server
The solution we propose begins with a timestamp server. A timestamp server works by taking
a hash of a block of items to be timestamped
and widely publishing the hash, such as in a
newspaper or Usenet post. The timestamp proves that the data must have existed at the
time, obviously, in order to get into the hash. Each timestamp includes the previous
timestamp in its hash, forming a chain, with each additional
timestamp reinforcing the ones before it.
4.Proof-of-Work
To implement a distributed timestamp server on a peer-to-peer basis, we will need to use
a proof- of-work system similar to Adam Back's Hashcash,
rather than newspaper or Usenet posts. The proof-of-work involves scanning for a
value that when hashed, such as with SHA-256, the
hash begins with a number of zero bits. The average work required is exponential in the
number of zero bits required and can be verified
by executing a single hash.
For our timestamp network, we implement the proof-of-work by incrementing a nonce in the
block until a value is found that gives the block's hash the required zero bits. Once
the CPU effort has been expended to make it satisfy
the proof-of-work, the block cannot be changed without redoing the work. As later blocks
are chained after it, the work to change the block
would include redoing all the blocks after it.
The proof-of-work also solves the problem of determining representation in majority
decision making. If the majority were based on one-IP-address-one-vote,
it could be subverted by anyone able to allocate many IPs. Proof-of-work is
essentially one-CPU-one-vote. The majority decision is represented by the longest chain,
which has the greatest proof-of-work effort invested
in it. If a majority of CPU power is controlled by honest nodes, the honest chain will grow
the fastest and outpace any competing chains.
To modify a past block, an attacker would have to
redo the proof-of-work of the block and all blocks after it and then catch up with and
surpass the work of the honest nodes. We will show later
that the probability of a slower attacker catching up
diminishes exponentially as subsequent blocks are added.
To compensate for increasing hardware speed and varying interest in running nodes over
time, the proof-of-work difficulty is determined
by a moving average targeting an average number of
blocks per hour. If they're generated too fast, the difficulty increases.
5.Network
The steps to run the network are as follows: 1) New transactions are broadcast to all nodes.
2) Each node collects new transactions into a block.
3) Each node works on finding a difficult proof-of-work for its block.
4) When a node finds a proof-of-work, it broadcasts the block to all nodes.
5) Nodes accept the block only if all transactions in it are valid and not already spent.
6) Nodes express their acceptance of the block by working on creating the next block in the
chain, using the hash of the accepted block as the previous hash.
Nodes always consider the longest chain to be the correct one and will keep working on
extending it. If two nodes broadcast different versions of the next block simultaneously,
some nodes may receive one or the other first.
In that case, they work on the first one they received,
but save the other branch in case it becomes longer. The tie will be broken when the next
proof- of-work is found and one branch becomes longer;
the nodes that were working on the other branch will then switch to the longer one.
New transaction broadcasts do not necessarily need to reach all nodes. As long as they reach
many nodes, they will get into a block before long. Block broadcasts are also tolerant of
dropped messages. If a node does not receive a block,
it will request it when it receives the next block and
realizes it missed one.
6. Incentive
By convention, the first transaction in a block is a special transaction that starts
a new coin owned by the creator of the block. This adds an
incentive for nodes to support the network, and provides
a way to initially distribute coins into circulation, since there is no central authority to issue
them. The steady addition of a constant of amount
of new coins is analogous to gold miners expending resources to add gold to circulation. In our
case, it is CPU time and electricity that is expended.
The incentive can also be funded with transaction fees. If the output value of a transaction
is less than its input value, the difference
is a transaction fee that is added to the incentive value of
the block containing the transaction. Once a predetermined number of coins have entered
circulation, the incentive can transition entirely to transaction fees and be completely
inflation free.
The incentive may help encourage nodes to stay honest. If a greedy attacker is able
to assemble more CPU power than all the honest
nodes, he would have to choose between using it
to defraud people by stealing back his payments, or using it to generate new coins. He ought
to find it more profitable to play by the rules,
such rules that favour him with more new coins than
everyone else combined, than to undermine the system and the validity of his own wealth.
7.Reclaiming Disk Space
Once the latest transaction in a coin is buried under enough blocks, the spent transactions
before it can be discarded to save disk space. To
facilitate this without breaking the block's hash,
transactions are hashed in a Merkle Tree, with only the root included in the block's
hash. Old blocks can then be compacted by stubbing
off branches of the tree. The interior hashes do
not need to be stored.
A block header with no transactions would be about 80 bytes. If we suppose blocks are
generated every 10 minutes, 80 bytes * 6 * 24 * 365 = 4.2MB per year. With computer systems
typically selling with 2GB of RAM as of 2008, and Moore's Law predicting current growth
of 1.2GB per year, storage should not be a problem
even if the block headers must be kept in memory.
8. Simplified Payment Verification
It is possible to verify payments without running a full network node. A user only needs
to keep a copy of the block headers of the longest
proof-of-work chain, which he can get by querying network nodes until he's convinced he has
the longest chain, and obtain the Merkle branch linking the transaction to the block it's
timestamped in. He can't check the transaction for
himself, but by linking it to a place in the chain, he can see that a network node has
accepted it, and blocks added after it further confirm
the network has accepted it. As such, the verification is reliable as long
as honest nodes control the network, but is more
vulnerable if the network is overpowered by an attacker. While network nodes can verify
transactions for themselves, the simplified method can be fooled by an attacker's fabricated
transactions for as long as the attacker can continue to overpower the network. One strategy
to protect against this would be to accept alerts
from network nodes when they detect an invalid block, prompting the user's software to download
the full block and alerted transactions to confirm the inconsistency. Businesses that
receive frequent payments will probably still want to
run their own nodes for more independent security and quicker verification.
9. Combining and Splitting Value
Although it would be possible to handle coins individually, it would be unwieldy to make
a separate transaction for every cent in a transfer.
To allow value to be split and combined, transactions contain multiple inputs and outputs.
Normally there will be either a single input from a larger previous transaction or multiple
inputs combining smaller amounts, and at most two
outputs: one for the payment, and one returning the change, if any, back to the sender.
It should be noted that fan-out, where a transaction depends on several transactions, and those
transactions depend on many more, is not a problem here. There is never the need to extract
a complete standalone copy of a transaction's
history.
10. Privacy
The traditional banking model achieves a level of privacy by limiting access to information
to the parties involved and the trusted third party.
The necessity to announce all transactions publicly
precludes this method, but privacy can still be maintained by breaking the flow of information
in another place: by keeping public keys anonymous.
The public can see that someone is sending an amount to someone else, but without information
linking the transaction to anyone. This is similar to the level of information released
by stock exchanges, where the time and size of
individual trades, the "tape", is made public, but without telling who the parties were.
As an additional firewall, a new key pair should be used for each transaction to keep
them from being linked to a common owner. Some
linking is still unavoidable with multi-input transactions, which necessarily reveal that
their inputs were owned by the same owner. The risk
is that if the owner of a key is revealed, linking could reveal other transactions that
belonged to the same owner.
11. Calculations
We consider the scenario of an attacker trying to generate an alternate chain faster than
the honest chain. Even if this is accomplished, it does
not throw the system open to arbitrary changes, such
as creating value out of thin air or taking money that never belonged to the attacker.
Nodes are not going to accept an invalid transaction
as payment, and honest nodes will never accept a block
containing them. An attacker can only try to change one of his own transactions to take
back money he recently spent.
The race between the honest chain and an attacker chain can be characterized as a Binomial
Random Walk. The success event is the honest chain being extended by one block, increasing
its lead by +1, and the failure event is the attacker's
chain being extended by one block, reducing the
gap by -1.
The probability of an attacker catching up from a given deficit is analogous to a Gambler's
Ruin problem. Suppose a gambler with unlimited credit starts at a deficit and plays potentially
an infinite number of trials to try to reach
breakeven. We can calculate the probability he ever
reaches breakeven, or that an attacker ever catches up with the honest chain, as follows:
And here there's some mathematics which you can look at at bitcoin.org/bitcoin.pdf
p= probability an honest node finds the next block
q1= probability the attacker finds the next block
qz= probability the attacker will ever catch up from z blocks behind
The probability drops exponentially as the number of blocks the
attacker has to catch up with increases. With the odds against him, if he doesn't make a
lucky lunge forward early on, his chances become
vanishingly small as he falls further behind. We now consider how long the recipient of
a new transaction needs to wait before being sufficiently certain the sender can't change
the transaction. We assume the sender is an attacker
who wants to make the recipient believe he paid him for a while, then switch it to pay
back to himself after some time has passed. The receiver
will be alerted when that happens, but the sender hopes it will be too late.
The receiver generates a new key pair and gives the public key to the sender shortly
before signing. This prevents the sender from preparing
a chain of blocks ahead of time by working on
it continuously until he is lucky enough to get far enough ahead, then executing the transaction
at that moment. Once the transaction is sent,
the dishonest sender starts working in secret on a
parallel chain containing an alternate version of his transaction.
The recipient waits until the transaction has been added to a block and z blocks have
been linked after it. He doesn't know the exact amount of progress the attacker has
made, but assuming the honest blocks took the average expected time per block, the attacker's
potential progress will be a Poisson distribution with expected value:
And here you can check the document, and realize with the equations and c code you will find
that the probability becomes enormously tiny.
12. Conclusion
We have proposed a system for electronic transactions without relying on trust. We started with
the usual framework of coins made from digital signatures, which provides strong control
of ownership, but is incomplete without a way
to prevent double-spending. To solve this, we
proposed a peer-to-peer network using proof-of-work to record a public history of transactions
that quickly becomes computationally impractical for an attacker to change if honest nodes
control a majority of CPU power. The network is robust in its unstructured simplicity.
Nodes work all at once with little coordination.
They do not need to be identified, since messages are
not routed to any particular place and only need to be delivered on a best effort basis.
Nodes can leave and rejoin the network at will, accepting
the proof-of-work chain as proof of what happened while they were gone. They vote with
their CPU power, expressing their acceptance of
valid blocks by working on extending them and rejecting invalid blocks by refusing to
work on them. Any needed rules and incentives can
be enforced with this consensus mechanism.
This is Stefan Molyneux from Freedomain Radio and I hope this has been very helpful, and
I encourage you to explore this very exciting world, of shared database information.